Well placement has been developed over the years by providing logging while drilling (LWD) measurements at the surface or above the subterranean formation in real time, starting with gamma ray and resistivity logs, and more recently deeper directional electromagnetic measurements. In addition, there has been increasing interest in providing additional formation evaluation data at the surface in real time, such as, for example, nuclear magnetic resonance (NMR) echo train measurements. The NMR measurements can provide information concerning porosity, the distribution of pore sizes, fluid typing, and fluid composition. NMR echo train measurements are very high dimensional and may include both Carr, Purcell, Meiboom, and Gill (CPMG) and enhanced precision mode (EPM) burst measurements that include thousands of echoes.
To make these NMR echo measurements available at the surface in real time, compression algorithms may be used to convert the NMR data into a bitstream that can be transmitted to the surface using, for example, a mud-pulse telemetry system. These compression algorithms may employ entropy encoding. Because of this entropy encoding, these bitstreams may be susceptible to various types of transmission errors that can cause errors in the NMR data reconstructed at the surface.